Prove the following statement "For Elevations which exceed or fal… - Vidyadip

Question

Prove the following statement "For Elevations which exceed or fall short of 45° by equal amounts, the ranges are equal”.

✓

Answer

Case I: When angle of projection
$\theta=45^\circ+\alpha$
Range, $\text{R}_1=\frac{\text{u}^2\sin2(45^\circ+\alpha)}{\text{g}}$
$=\frac{\text{u}^2\cos2\alpha}{\text{g}}$
Case II: When angle of projection
$\theta=45^\circ-\alpha$
Range, $\text{R}_2=\frac{\text{u}^2\sin2(45^\circ-\alpha)}{\text{g}}$
$=\frac{\text{u}^2}{\text{g}}\sin(90^\circ-2\alpha)$
$=\frac{\text{u}^2\cos2\alpha}{\text{g}}=\text{R}_1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Motion in a Plane→Motion in a Plane — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):

$\sin\omega\text{t}-\cos\omega\text{t}$

The speed of sound as measured by a student in the laboratory on a winter day is 340m/s when the room temperature is 17^°C. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32^°C?

When a ball is thrown upward, its momentum first decreases and then increases. Does this violate the principle of conservation of momentum?

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
What is the final pressure of the gas in A and B?

An astronaut, by mistake, drops his food packet from an artificial satellite orbiting around the earth. Will it reach the surface of the earth? Why?

A bullet going with speed 350m/s enters a concrete wall and penetrates a distance of 5.0cm before coming to rest. Find the deceleration.

Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river? Explain.

Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young’s Modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.

A person is painting his house walls. He stands on a ladder with a bucket containing paint in one hand and a brush in other. Suddenly the bucket slips from his hand and falls down on the floor. If the bucket with the paint had a mass of 6.0kg and was at a height of 2.0m at the time it slipped, how much gravitational potential energy is lost together with the paint?

If the units of force, energy and velocity are $20 N, 200 J$ and $5 ms^{-1}$, find the units of length, mass and time.

→